Goodness! Almost a day later, and noone has responded.
Very well described.
I can offer some motherly, rule-of-thumb advice for infections in general.
Since we're talking about an eye, if it's getting worse or staying the same, go to your doctor.
If it is at all smaller, continue what you're doing.
Don't guilt-trip yourself over possible uncleanliness being the cause. It's a germ.
Either you had some contact (including air-borne), and/or your resistance is low (e.g, lack of sleep, poor diet, stress).
For "compresses," I used cotton balls dipped in Eyebrite tea when my kids were young--often on my own eye when I felt like I was catching something from one of them. It worked well for me.
More recently I did the hot, wet, wash cloth routine with much success for a bump on the part of the eyelid not-so-near the eye.
You get A++ for not squeezing.
Cats can carry some people germs. Then, if you pet him, followed by wiping some leaf-blower gunk out of your eye....
Washing your pillow case daily at this time is a good idea, though normally what you're doing should be fine.